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Total vertex irregular labeling of complete bipartite graphs. (English) Zbl 1100.05090
A total vertex irregular labeling on a graph $$G$$ is an assignment of integer labels to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of $$G$$ is the minimum value of the largest label over all such irregular assignments. The paper gives the total vertex irregularity strength of certain complete bipartite graphs, and shows that, in general, it is greater than a certain value.

##### MSC:
 05C78 Graph labelling (graceful graphs, bandwidth, etc.)